Why did Apple sign me up for $10 per month Music without my permission?

It's more likely that someone used your credit card if your bank alerted you. Regardless visit support.apple.com/billing for any billing issues and to review your purchases and subscriptions. If you see nothing, use the "get support" link on the page to speak with Apple Support. And, finally, cancel your credit card.

They didn't. You likely had a trial that converted into a subscription or subscribed yourself. Visit support.apple.com/billing.

No, they signed themself up. You just see the charge but don't have access. Again, if you have access, cancel your subscription. Visit support.apple.com/billing.

Believe what you want to but your knee jerk reaction accusing Apple of deception and fraud is total nonsense. You should be contacting your bank to investigate. But whatever.